Linear Projective Groups

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Related lectures (30)

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The Torus and Linear Groups

Explores the torus, linear groups, stability properties of matrices, and homomorphisms.

Linear algebraic groups

Covers linear algebraic groups, including special sets and matrix examples.

Symplectic Groups

Explores symplectic groups, linear transformations preserving non-degenerate alternating bilinear forms on vector spaces.

Self-similar groups II

Explores self-similar groups acting on rooted trees and their properties.

Matrix Operations: Scaling and Invertibility

Covers scaled matrices, ladder matrices, and the Gauss method for matrix operations.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Explores dynamics on homogeneous spaces and their interactions with number theory, focusing on modular lattices and the Iwasawa decomposition theorem.

Group Actions: Examples

Showcases examples of group actions on vector spaces and topological spaces.

Conductor of X: Waldsparger Formula and Subconvexity Bound

Covers the equidistribution of representations of integers by ternary forms and the conductor of X.

Linear Algebra: Elementary Row Operations

Covers elementary row operations, equivalent matrices, invertibility, and bases in linear algebra.

3D Rotations and Quaternions

Covers 3D rotations, quaternions, and matrices of direction cosines, providing an elegant solution to the limitations of rotation matrices.